Question

Show that the line segment joining the mid points of the opposite sides of a quadrilateral bisect

each other​

Answer 1

$\huge \fbox \purple{Answer:-}$

ABCD is a quadrilateral such that P, Q, R and s are the mid points of sides AB, BC, CD and DA respectively. (see the image)

In ABC, P and Q are the mid points of sides AB and BC respectively.

• Therefore, PQ || AC and PQ = 1/2 of AC

• Similarly, RS || AC and RS = 1/2 of AC

• PQ || RS and PQ = RS

• Similarly, PQ || QR and PQ = QR

Hence, PQRS is a parallelogram.

Since the diagonals of a parallelogram bisect each other,

PR and QS bisect each other.

Answer 2

Answer:

According to the given condition P,Q,R,S are midpoints.

therefore in triangle ABC

S and R are midpoints

therefore by midpoint theorem

SR is parallel to AC and SR=1/2AC (I)

Similarly

In triangle ADC

p and Q are midpoints

by midpoint theorem

PQ is parallel to AC and PQ=1/2AC. (II)

therefore from (I) and (II) we get

PQ is parallel to SR and PQ = SR

Since the opposite sides are equal and parallel

therefore PQRS is a parallelogram

therefore PR and SQ bisect each other [ digonals of a parallelogram bisect each other]

Hence proved

Hope it helps